Phase Diagrams

The Stabilities of phase
What is a phase?
A phase is a form of matter that is uniform throughout in chemical composition and physical state
Example
Fig 1. White phosphorus
Fig 2.Black phosphorus
Fig 3. Liquid phase
A phase transition is the spontaneous conversion of one phase into another phase,occurs at a characteristic temperature for a given presure
Example
At 1 atm
Below 00C
Ice
Above 00C
Liquid water
Fig 4. The example of phase transition
The transition temperature,Ttrs, is the temperature at which the two phase are in equilibrium and the Gibbs energy is minimized at the prevailing presure
Example
Fig 5. The transition temperature of water
A metastable phase is a thermodynamically unstable phase that persists because the transition is kinetically hindered
Example
Diamond Fig 6. Metastable phase of carbon
Graphite Fig 7. A metastable systems diagram Phase boundaries
A phase diagram is a diagram show the regions of pressure and temperature at which its various phase are thermodynamically stable
Fig 8. A typical phase diagrams
Fig 10. The boiling process
Heat
The temperature at which the vapour pressure of a liquid is equal to the external pressure is called the boiling temperature
Fig 9. The experiment about vapour pressure
Heat
Heat
Fig 11. The experiment about critical temperature The temperature at which the surface disappear is the critical temperature
Melting
Freezing
The melting temperature (or freezing temperature) is the temperature at which, under the specified pressure, the liquid and solid phases of a substance coexist in equilibrium Phase Diagrams
ISSUES TO ADDRESS...
• When we combine two elements...
what equilibrium state do we get?
• In particular, if we specify...
‐‐a composition (e.g., wt% Cu ‐ wt% Ni), and
‐‐a temperature (T)
then...
How many phases do we get?
What is the composition of each phase?
How much of each phase do we get?
Phase B
Phase A
Nickel atom
Copper atom
Phase Equilibria: Solubility Limit
Introduction
– Solutions – solid solutions, single phase
– Mixtures – more than one phase
Sucrose/Water Phase Diagram
• Solubility Limit:
Answer: 65 wt% sugar.
If Co < 65 wt% sugar: syrup
If Co > 65 wt% sugar: syrup + sugar.
60
L
40
(liquid solution i.e., syrup)
20
0
L
(liquid) + S
(solid sugar)
20
40
60 65 80
Co =Composition (wt% sugar)
100
Pure Sugar
solubility limit at 20°C?
Solubility Limit
80
Pure Water
Question: What is the
10 0
Temperature (°C)
Max concentration for
which only a single phase solution occurs.
Components and Phases
• Components:
The elements or compounds which are present in the mixture
(e.g., Al and Cu)
• Phases:
The physically and chemically distinct material regions
that result (e.g., α and β).
Aluminum‐
Copper
Alloy
β (lighter phase)
α (darker phase)
Effect of T & Composition (Co)
• Changing T can change # of phases: • Changing Co can change # of phases:
path A to B.
path B to D.
B (100°C,70)
1 phase D (100°C,90)
2 phases water‐
sugar
system
Temperature (°C)
100
80
L
60
(liquid) + L
(liquid solution 40
i.e., syrup)
20
0
0
S
(solid sugar)
A (20°C,70)
2 phases
20
40
60 70 80
Co =Composition (wt% sugar)
100
Phase Equilibria
Simple solution system (e.g., Ni‐Cu solution)
Crystal
Structure
electro
negativity
r (nm)
Ni
FCC
1.9
0.1246
Cu
FCC
1.8
0.1278
•Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume –
Rothery rules) suggesting high mutual solubility. • Ni and Cu are totally miscible in all proportions.
Phase Diagrams
• Indicate phases as function of T, Co, and P. • For this course:
‐binary systems: just 2 components.
‐independent variables: T and Co (P = 1 atm is almost always used).
• Phase
Diagram
for Cu‐Ni
system
T(°C)
1600
• 2 phases:
1500
L (liquid)
α (FCC solid solution)
L (liquid)
• 3 phase fields: L
L+ α
α
1400
1300
α
1200
(FCC solid 1100
1000
solution)
0
20
40
60
80
100 wt% Ni
Phase Diagrams:
# and types of phases
• Rule 1:
If we know T and Co, then we know:
‐‐the # and types of phases present.
T(°C)
1600
• Examples:
B (1250°C,35)
1500
A(1100°C, 60): 1 phase: α
B (1250°C, 35): 2 phases: L + L (liquid)
1400
α
1300
1200
α
(FCC solid solution)
A(1100°C,60)
1100
1000
Cu‐Ni
phase
diagram
0
20
40
60
80
100 wt% Ni
Phase Diagrams:
composition of phases
• Rule 2:
If we know T and Co, then we know:
‐‐the composition of each phase.
• Examples:
C o = 35 wt% Ni
At T A = 1320°C: Only Liquid (L) C L = C o ( = 35 wt% Ni)
At T D = 1190°C: Only Solid ( α) C α = C o ( = 35 wt% Ni )
Cu‐Ni system
T(°C)
A
TA
L (liquid)
1300
B
TB
1200
D
TD
At T B = 1250°C: Both α and L
C L = C liquidus ( = 32 wt% Ni here) C α = C solidus ( = 43 wt% Ni here)
tie line
20
3032
35
C LC o
α
(solid)
40 4 3
50
C α wt% Ni
Phase Diagrams:
weight fractions of phases
• Rule 3:
If we know T and Co, then we know:
‐‐the amount of each phase (given in wt%).
• Examples:
C o = 35 wt% Ni
At T A : Only Liquid (L) W L = 100 wt%, W α = 0
At T D : Only Solid ( α) W L = 0, W α = 100 wt%
At T B : Both α and L
WL
=
Wα =
43 − 35
=
= 73 wt %
R + S
43 − 32
S
R
R + S
T(°C)
A
TA
1300
TB
tie line
L (liquid)
B
R
1200
S
D
TD
20
= 27 wt%
Cu‐Ni system
3 032
35
C LC o
α
(solid)
4043
50
C α wt% Ni
The Lever Rule
• Tie line – connects the phases in equilibrium with each other ‐ essentially an isotherm
T(°C)
How much of each phase? Think of it as a lever
tie line
1300
L (liquid)
B
TB
α
(solid)
1200
R
20
30C
S
40 C
α
L Co
R
50
wt% Ni
WL =
Mα
ML
C − C0
ML
S
=
= α
M L + M α R + S C α − CL
S
M α ⋅S = M L ⋅R
Wα =
C − CL
R
= 0
R + S C α − CL
Fe‐Fe3C System
21